NF-Build+fractions+from+unit+fractions+by+applying+&+extending+previous+understandings+of+operations+on+whole+numbers

Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. 4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 4.NF.4.Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? || ===‍‍‍‍‍‍Anchor Standard/Mathematical Practice(s) === MP.1. Make sense of problems and persevere in solving them. MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.6. Attend to precision. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">MP.7. Look for and make use of structure. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">MP.8. Look for and express regularity in repeated reasoning. || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Use technology tools and skills to reinforce classroom concepts and activities. || ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Revised Bloom's Level of thinking === <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Remembering <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Understanding || ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Learning Target/Task Analysis === <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.NF.3 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">A fraction with a numerator of one is called a unit fraction. When students investigate fractions other than <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">unit fractions, such as 2/3, they should be able to decompose the non-unit fraction into a combination of <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">several unit fractions. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: 2/3 = 1/3 + 1/3 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Being able to visualize this decomposition into unit fractions helps students when adding or subtracting <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">fractions. Students need multiple opportunities to work with mixed numbers and be able to decompose <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">them in more than one way. Students may use visual models to help develop this understanding. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> 1 ¼ - ¾ = <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4/4 + ¼ = 5/4 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">5/4 – ¾ = 2/4 or ½ <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example of word problem: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">the pizza did the girls eat together? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Solution: The amount of pizza Mary ate can be thought of a 3/6 or 1/6 and 1/6 and 1/6. The amount <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">of pizza Lacey ate can be thought of a 1/6 and 1/6. The total amount of pizza they ate is 1/6 + 1/6 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">+ 1/6 + 1/6 + 1/6 or 5/6 of the whole pizza. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">A separate algorithm for mixed numbers in addition and subtraction is not necessary. Students <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">will tend to add or subtract the whole numbers first and then work with the fractions using the <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">same strategies they have applied to problems that contained only fractions. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">and Avery has 5 3/8 feet of ribbon. How much ribbon do they have altogether? Will it be enough to <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">complete the project? Explain why or why not. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">The student thinks: I can add the ribbon Susan has to the ribbon Avery has to find out how much ribbon <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">they have altogether. Susan has 3 1/8 feet of ribbon and Avery has 5 3/8 feet of ribbon. I can write this as <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">3 1/8 + 5 3/8. I know they have 8 feet of ribbon by adding the 3 and 5. They also have 1/8 and 3/8 which <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">makes a total of 4/8 more. Altogether they have 8 4/8 feet of ribbon. 8 4/8 is larger than 8 3/8 so they will <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">have enough ribbon to complete the project. They will even have a little extra ribbon left, 1/8 foot. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Example: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">has 2 4/8 of a pizza left. How much pizza did Timothy give to his friend? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Solution: Timothy had 4 1/8 pizzas to start. This is 33/8 of a pizza. The x’s show the pizza he has left which <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">is 2 4/8 pizzas or 20/8 pizzas. The shaded rectangles without the x’s are the pizza he gave to his friend <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">which is 13/8 or 1 5/8 pizzas. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Mixed numbers are introduced for the first time in Fourth Grade. Students should have ample experiences <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">of adding and subtracting mixed numbers where they work with mixed numbers or convert mixed numbers <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">into improper fractions. Keep in mind Concrete-Representation-Abstract (CRA) approach to teaching <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">fractions. Students need to be able to ―show‖ their thinking using concrete and/or representations BEFORE <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">they move to abstract thinking. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">4.NF.4 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Students need many opportunities to work with problems in context to understand the connections between <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">models and corresponding equations. Contexts involving a whole number times a fraction lend themselves <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">to modeling and examining patterns. This standard builds on students’ work of adding fractions and <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">extending that work into multiplication. (4.NF.4a) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard extends the idea of multiplication as repeated addition (4.NF.4b) For example, <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">3 x (2/5) = 2/5 + 2/5 + 2/5= 6/5 = 6 X (1/5). Students are expected to use and create visual fraction <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">models to multiply a whole number by a fraction. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">This standard calls for students to use visual fraction models (Area, Linear and Set Models) to solve word <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">problems related to multiplying a whole number by a fraction. (4.NF.4c)
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Common Core Standards ===
 * ===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Information Technology Standard ===
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Mary and Lacey decide to share a pizza. Mary ate 3/6 and Lacey ate 2/6 of the pizza. How much of
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Susan and Avery need 8 3/8 feet of ribbon to package gift baskets. Susan has 3 1/8 feet of ribbon
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Timothy has 4 1/8 pizzas left over from his soccer party. After giving some pizza to his friend, he

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍I can... <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can join fractions with a numerator of 1 and the same denominator by adding them. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can separate fractions with the same denominator by subtracting them. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can dissect fractions using fraction models. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can write a decomposed fraction (broken apart) using an equation. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can add and subtract mixed numbers with like denominators. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can determine which operation (addition or subtraction) to use when solving word problems involving fractions with like denominators. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can multiply a fraction with a numerator of 1 by a whole number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can multiply a fraction with a numerator greater than one by a whole number. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">I can solve word problems that involve multiplying a fraction by a whole number.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Illustrate adding and subtracting of fractions and mixed numbers using number lines, fraction strips, area models, set models, rulers, etc. Illustrate decomposing of fractions and mixed numbers with number lines, fraction strips, area models, set models, rulers, etc.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Solve. Simplify your answer.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">5 x 1/4 =

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">a×16=76

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">6×23=

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Problem Task:

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Draw a picture to explain why 85=8×15.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Kathy is having a party. She wants 23cups of trail mix per guest. She expects 6 guests. How much trail mix should Kathy prepare? Write an equation and justify your solution with a visual model. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• Draw a picture to show why these equations are true, and explain your reasoning: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">7/8 = 4/8 + 3/8 214 = 34 + 64 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• Sally said that 1/10 + 7/10 + 4/10 is the same as 1210. Is she correct? Explain and use a model to illustrate your explanation. (This is for Standard 4.c.) <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">• Draw a model of the garden plot according to the data table below. The plot is divided into 15 sections. What fraction of the plot will be potatoes? <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Crop Number of sections <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Corn 4 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Peas 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Strawberries 2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Tomatoes 3 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Potatoes The rest

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Adding and Subtracting Fractions

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Intervention:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">DPI Classroom Strategies p. 22

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Letter R--Have students work in groups to make fraction/decimal dominoes. One end has a picture; the other has the fraction and/or decimal notation. On the other side they could write the number/fraction out in word or expanded form and they could also write a story problem.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">http://daretodifferentiate.wikispaces.com/Choice+Boards

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Enrichment:
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Have students write in their journal how they could share lunch with two or friends (Or) write how knowing fractions helps you play a musical instrument.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Near Zero, About ½ and Close to 1. Pass out index cards with decimal numbers. Students would work with partners to convert the decimal to a fraction and place your card in the correct bucket.

===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">Have students write in their journal how they could share lunch with two or friends (Or) write how knowing fractions helps you play a musical instrument. ===

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Instructional Resources
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">[] <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">[]

===<span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">‍‍‍‍‍‍Notes and Additional Information === <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">[] <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 110%; line-height: 0px; overflow: hidden;">